# Improper fractions - Definition, Steps, Examples & Practice Questions (2023)

Improper fractions, with the name, signifying that the fractions are not done in a proper manner for any number, object or element. In Maths, a fraction is a part of a whole. Fractions have two parts, numerator and denominator. If ⅓ is a fraction, then 1 is the numerator, and 3 is the denominator. An improper fraction has a numerator greater than the denominator. For example, 3/2 is an improper fraction, but 2/3 is a proper fraction, whosedenominator is greater than the numerator.

In this article, you will find all the topics related to improper fractions. Also, we perform various arithmetic operations on these fractions, such as addition, division, multiplication, etc.

• Definition
• Simplification
• Improper fraction to Mixed Fractions
• Mixed to Improper fraction
• Subtraction of Improper fraction
• Solved Examples
• Video Lesson
• Practise Questions
• FAQs

## What are Improper Fractions?

An improper fraction is defined as a fraction whose numerator is greater than the denominator. Suppose, x/y is an improper fraction, such that x > y. It is therefore, the improper fraction is always greater than one.

Examples of Improper Fractions are:

• 17/5
• 9/4
• 13/4
• 16/3
• 5/2

## How to Simplify Improper Fractions?

We have understood what an improper fraction is. Now, let us discuss here how to simplify such fractions here.

• Step 1: Determine if the given fraction is improper or not.
• Step 2: Now interpret the denominator and check for how many parts it is dividing the numerator.
• Step 3: Check the common factors of numerator and denominator
• Step 4: Cancel the like terms both from numerator and denominator.

The resulted fraction is the simplified fraction. Let us understand these steps with the help of examples.

Example: Simplify the fraction 24/10.

Solution: Since we know 24>10, thus 24/10 is an improper fraction.

Let us factorise the numerator and denominator.

24 = 2 x 2 x 2 x 3

10 = 2 x 5

Since we can see 2 is the common factor for 24 and 10, so after cancelling 2 from the numerator and denominator, we get;

(2 x 2 x 3)/5 = 12/5

## Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, divide the denominator by the numerator. The quotient becomes the whole number, the remainder will be the numerator, and the divisor becomes the denominator.

Let us consider an example. Convert 17/4 to a mixed fraction.

When we divide 17 by 4, the quotient is 4 and the remainder is 1. So the mixed fraction is 4 1/4.

Although an improper fraction can be converted to a mixed fraction, there are situations where expressing a fraction as an improper fraction minimizes a lot of confusion, especially when the fractions are expressed in calculations.

For example, consider 3 + 6 2/3.

Is it 3 + 6 + 2/3 or3 + 6 × 2/3 ?

(Video) Improper Fractions & Mixed Numbers | Learning Maths

This confusion can be removed by writing it as 3 + 20/3.

## Mixed to Improper Fraction

Let us say 31/4 is a mixed fraction to be converted into an improper fraction.
Multiply 4 by 3 and add with the numerator 1, we get;
4 x 3 + 1 = 13
Hence, the required numerator of the improper fraction is 13 while the denominator remains the same, i.e., 4
Therefore, the required fraction is 13/4

Another Method:
Write the mixed number as a sum of the whole number and proper fraction, such that;
3 + ¼
Now rationalise the denominators and write the two parts with a common denominator.
12/4 + ¼
13/4

The addition of improper fractions can have two scenarios. If the denominators of all the fractions are equal, we can add all the numerators and keep the same denominator.

For example, (17/4) + (9/4) + (5/4)

Since the denominator of all three fractions is equal, we add all the numerators by keeping the common denominator as 4.

Hence, we get the following:

(17/4) + (9/4) + (5/4) = (17 + 9 + 5) / 4

(17/4) + (9/4) + (5/4) = 31/4.

The other case is thatdenominators of fractions are not equal. Here, the process is slightly different and involves the calculation of the least common multiple of the denominators.

You can learn the calculation of the least common multiples here.

Consider the example, (15/3) + (3/4) + (5/2)

Here, the denominators of the fractions are different. (i.e., 3, 4, 2), and take the LCM of 2, 3, and 4.

• The least common multiple of 3, 4, and 2 is 12.
• Now the fraction we get by adding all these fractions will have 12 as the denominator.
• Divide the LCM by each of the denominators and multiply the quotient by the numerators.
• The numerator of the new fraction will be the sum of all the numbers obtained in the previous step.
• Now, in the first fraction, the denominator is 3. LCM 12 divided by 3 is 4. The numerator is 15. 15 x 4 is 60. Similarly, for the other two fractions, the numbers are 9, and 30.

Therefore,(15/3) + (3/4) + (5/2) = (60/12) + (9/12) + (30/12)

(15/3) + (3/4) + (5/2) = (60 + 9 + 30) / 12

(15/3) + (3/4) + (5/2) = 99/12.

Now, the sum of fractions can be simplified as:

(15/3) + (3/4) + (5/2) = 33/4

convert into mixed fractions, if required.

Hence, the mixed fraction is:

(Video) Improper Fractions to Partial Fractions (unequal degree) : ExamSolutions Maths Revision

(15/3) + (3/4) + (5/2) = 8 1/4.

## Subtraction of Improper Fractions

In a similar manner, as we added the improper fractions, we can also subtract them.

• The first step is to check if denominators are the same or not
• The second is to rationalise the denominators
• The last step is to subtract the given fractions and simply, if required

Let us see an example:

Subtract 5/2 – 7/3.

LCM (2,3) = 6

Therefore,

(5/2 x 3/3) – (7/3 x 2/2)

= 15/6 – 14/6

= (15-14)/6

= 1/6.

## Related Articles

 Comparing Fractions – An Overview Multiplication of Fractions Fractions Addition And Subtraction Of Fractions

## Solved Examples of Improper Fractions

Example 1:

Multiply 3 by 9/7.

Solution:

Given: 3 x 9/7

3 x 9/7 = 27/7

Example 2:

Convert the improper fraction 5/4 into a mixed fraction.

Solution:

Given, 5/4

To convert an improper fraction into a mixed fraction, first, divide the number 5 by 4.

(Video) Algebraic Fractions : Improper fractions to mixed fractions : ExamSolutions

If we divide 5 by 4, we get the quotient as 1 and the remainder as 1.

Hence, keep the quotient as the whole number part and the remainder as the fraction’s numerator part and the denominator as 4.

Hence, 5/4 written in the mixed fraction is 1 1/4.

i.e., 5/4 = 1 1/4.

Example 3:

Convert the mixed number 4 2/3 into an improper fraction.

Solution:

Given: Mixed fraction = 4 2/3

To convert the mixed fraction into an improper fraction, follow the below steps:

Step 1: Multiply 3 by 4, and we get 12.

Step 2: Now, add 12 and 2, we get 14

I,e 3(4) + 2 =14

Now, put the number 14 in the fraction’s numerator and keep the number 3 as the denominator.

So, 14/3 is the required fraction.

Example 4:

Write 3 1/4as an improper fraction.

Solution:

Given that 3 1/4is a mixed number.

Now, multiply denominator 4 by the whole number 3.

4 × 3 = 12

Now, add 12 to the numerator.

(Video) Improper Fractions to Mixed Numbers | How to Convert | Math with Mr. J

12 + 1 = 13

Hence, 13 is the new numerator of the improper fraction, whereas the denominator remains the same.

So,

3 1/4= 13/4

## Video Lesson ## Practice Questions

Convert the given improper fractions into mixed numbers.

• 9/2 = ?
• 12/5 = ?
• 22/9 = ?
• 19/7 = ?
• 20/9 = ?

Convert into improper fractions.

• 4 1/2 = ?
• 7 ⅓ = ?
• 4 ⅖ = ?
• 6 1/9 = ?
• 4 ⅞ = ?

Learning about fractions can be so much fun. Download BYJU’S – The Learning App and discover innovative ways to learn science and math.

## Frequently Asked Questions on Improper Fraction

### What is an Improper fraction? Give examples.

A fraction is called improper if the numerator is greater than the denominator. Examples are 9/2, 8/5, 10/3, etc.

### How to convert an improper fraction into a mixed fraction?

Divide the numerator by denominator. Write the whole number separately and put the remainder in the numerator. If 11/4 is a fraction, then;
11 divided by 4 = 2 + 3 remainder
Therefore, 11/4 = 2 3/4

### Convert 1 ⅔ as an improper fraction?

Multiply 3 by 1 and add 2 to get the denominator of the required fraction and keep the denominator common.
1 ⅔ = (3 x 1 + 2)/3 = 5/3

### What is the difference between proper and improper fractions?

A proper fraction has a numerator smaller than the denominator, but an improper fraction has a denominator smaller than the numerator.

### Solve 3 1/5.

3 ⅕ = (5 x 3 + 1)/5 = 16/5

(Video) Math Antics - Mixed Numbers

## FAQs

### What is improper fraction with example and answer? ›

An improper fraction has a numerator greater than the denominator. For example, 3/2 is an improper fraction, but 2/3 is a proper fraction, whose denominator is greater than the numerator.

What are some examples of improper fraction? ›

An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

What is improper fraction short answer? ›

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

What is an improper fraction explain? ›

Improper fractions: Improper fractions are defined as fractions for which the numerator is greater than the denominator.

How do I find the improper fraction? ›

Explanation: To determine the numerator of the improper fraction, multiply the denominator with the whole number. Then add this with the numerator. The denominator will remain the same.

Which of the following is improper fraction answer? ›

An improper fraction is a fraction whose numerator is greater than the denominator. Hence, here 72 and 53 are improper fractions.

What is improper fraction explained to kids? ›

An improper fraction is a fraction whose top number (numerator) is larger than the bottom number (denominator). An improper fraction isn't wrong, but since the numerator, which represents the parts of the whole, is larger, the fraction actually represents a whole number and a fraction.

How do you simplify improper fractions for kids? ›

How to Simplify Improper Fractions
1. Identify a common factor (a number that multiplies with another to make your given number) of both the numerator and denominator.
2. Divide the numerator and the denominator by that same factor.
3. You have a simplified fraction. Congratulations.

Which is an example of an improper fraction quizlet? ›

An "improper fraction" has a numerator that is greater than or equal to its denominator. A "mixed number" shows the sum of a whole number and a proper fraction. Write 6 2/3 as an improper fraction.

What are the 3 steps for changing a mixed number into an improper fraction? ›

To change a mixed number to an improper fraction, follow these steps:
1. Multiply the whole number by the denominator.
2. Add that number to the numerator.
3. Write that sum on top of the original denominator.

### What is 4 and 2/3 as a improper fraction? ›

Answer and Explanation: Three improper fractions for 4 2/3 are 14/3, 28/6, and 42/9. To find these, first convert the mixed number 4 2/3 to a fraction.

What is proper fraction examples with answers? ›

A fraction in which the numerator value is always less than the denominator value is known as a proper fraction. For example, 18/25, 19/45, 62/78, 1/6, 1/9, are proper fractions.

What is 7 and 3/4 as an improper fraction? ›

The mixed number 7 3/4 can be changed into the improper fraction 31/4.

Is 4 4 an improper fraction? ›

For example 4/4 ? Well, it is obviously the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction.

What is 5 ¾ as an improper fraction? ›

Answer and Explanation: The improper fraction that is equivalent to the mixed number 5 3/4 is 23/4.

What is 7 4 5 as an improper fraction? ›

So, 7 4/5 is equal to the improper fraction 39/5.

What is 1 7 8 as a improper fraction? ›

Answer and Explanation: 1 7/8 can be converted to the improper fraction 15/8.

What are the 7 types of fractions with examples? ›

Every fraction comprises two numbers: a top number and a bottom number separated by a horizontal bar. These are known as the numerator and denominator, respectively, in Mathematics. There are 7 kinds of fractions: proper, improper, mixed, unit, equivalent, like and unlike fractions.

What is 2 5 6 as an improper fraction? ›

To convert a mixed fraction to an improper fraction, we have to calculate (2 + 5/6). 2 + 5/6 = (12 + 5) / 6 = 17/6. Hence, 2 5/6 as a fraction is equal to 17/6.

What is 5 and 7/8 as an improper fraction? ›

As an improper fraction, the mixed number 578 5 7 8 is 478 . To change a mixed number to an improper fraction, you do not have to change the denominator of the fraction.

### What is 5 2 3 as an improper fraction? ›

Answer and Explanation: The mixed number 5 2/3 is the same as the improper fraction 17/3.

Is 5 5 an improper fraction? ›

In the fraction 5/5, the numerator and denominator are equal. This means the numerator is not less than the denominator, so it is an improper fraction.

What is 3 and 3/4 as an improper fraction? ›

Answer and Explanation: The improper fraction 15/4 is equivalent to the mixed fraction 3 3/4.

Is 7 4 is a improper fraction? ›

Explanation: 7/4 is an improper fraction. Let's take the numerator and divide it by the denominator.

## Videos

1. Modeling Improper Fractions and Mixed Numbers | Math with Mr. J
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2. Improper Fractions | Learn with BYJU'S
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3. Proper and improper fractions | Fractions | Pre-Algebra | Khan Academy
4. Mixed Fractions and Improper Fractions - with oranges. Maths made clear with Dr Nic
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5. Review of Improper Fractions - 5th Grade Math
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Last Updated: 02/10/2023

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